Multivariate spatio-temporal modeling has become a very active research area in many scientific fields, including climate, hydrology, and ecology, due to its capacity to capture the space-time characteristics of data and provide accurate statistical inference.
For example, [1]} used multivariate spatio-temporal models to uncover forest composition in history based on fossil pollen records; [2]} used a multivariate spatio-temporal Gaussian Markov random field to assess Antarctica's mass balance and contribution to the rise of sea-level;
[3]} used a multivariate spatio-temporal model in a Bayesian hierarchical framework to investigate the extreme temperatures and precipitation jointly.
Gaussian random fields are widely used in geostatistics, directly representing the variables used in the study or serving as a building block in more complex statistical models, where the covariance structure plays a key role in quantifying dependence and providing prediction.
[4]} developed valid Matérn covariance functions for multivariate spatial random fields. [5]} proposed new approaches to build valid multivariate spatio-temporal covariance models via latent dimensions. [6]} reviewed approaches to build cross-covariance functions for multivariate random fields.
